度量空间的共轭维数及其收敛性

IF 0.4 4区数学 Q4 MATHEMATICS

Kodai Mathematical Journal Pub Date : 2019-11-18 DOI:10.2996/kmj/1605063629

Yoshito Ishiki

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引用次数: 4

摘要

我们引入了度量空间的伪锥的概念，作为切锥和渐近锥的推广。我们证明了度量空间的Assouad维数是由它的任何伪锥的Assouard维数从下定界的。我们给出了一个包含所有紧致度量空间作为伪锥的例子，以及包含所有适当长度空间作为切锥或渐近锥的例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Assouad dimension and convergence of metric spaces

We introduce the notion of pseudo-cones of metric spaces as a generalization of both of the tangent cones and the asymptotic cones. We prove that the Assouad dimension of a metric space is bounded from below by that of any pseudo-cone of it. We exhibit a example containing all compact metric spaces as pseudo-cones, and examples containing all proper length spaces as tangent cones or asymptotic cones.

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来源期刊

Kodai Mathematical Journal 数学-数学

CiteScore

0.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Kodai Mathematical Journal is edited by the Department of Mathematics, Tokyo Institute of Technology. The journal was issued from 1949 until 1977 as Kodai Mathematical Seminar Reports, and was renewed in 1978 under the present name. The journal is published three times yearly and includes original papers in mathematics.